To add a little more to the discussion:
Something else to consider is that a pump, ANY pump, be it fuel, oil, or air, takes a given amount of horsepower to move a given amount of fluid at a given flow rate.
ACCELERATING this pump from a low flow rate to a higher flow rate takes a great deal more power than operating it at steady state. The faster you wish accelerate this pump, the more power it takes.
This is critically important when speaking about superchargers on race cars, because, unfortunately, they don't operate at steady state for very long. The faster we wish to accelerate the engine, the faster the blower must accelerate as well (it's tied to the crank snout, after all). And, since the power requirement to accelerate the blower increases non-linearly, that blower better be able to keep up when it's called upon.
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